Nothing in military history quite matches the Roman standards. Perhaps the closest equivalent are the regimental colours in contemporary armies.

The standards, the signa were a recognition signal and a rallying point within the chaos of a battle field.

The various units of a Roman army required a device to recognize, watch and follow in the heat of battle. For this it was highly important that they recognized their own at a glance.

But much more than a mere means of identification, the Roman standards were held in awe. They were potent symbols of Roman honour. Not merely did they represent the honour of the unit, as with later regimental colours, but they represented the honour of Rome herself.

The aquila

One of the reasons for the Roman campaign in Germania following the defeat of Varus in the Teutoburger Wald was for the army to recover the lost standards of the defeated legions. Emperor Augustus also threatened war against Persia to ensure the standards last at Carrhae by Crassus were returned.

The standards were also of importance in pitching and striking camp. The first act of setting up camp was to stake the standards into the ground. The standards were afforded their own tent at the very heart of the camp itself, next to the tent of the commanding officer. When striking camps the standards were drawn fro the ground. For the standards to remain stuck fast within the earth was deemed a serious omen and the soldiers, ever superstitious, might even refuse their orders to move, lest they offend the will of the gods.

The standards also played key roles at religious festivals. On these occasions they would be anointed with precious oils and decorated with garlands. So revered were the standards during such ceremonies, that it might be argued the standards themselves were worshipped by the troops.

Caesar often referred to troops as ante and post signani; in front of and behind the standards. Given that the basic signum standard was for each maniple that consisted of two centuries, this suggests the standard tended to be kept between the two, the rear century commanded by the posterior centurion and the front century by the prior centurion. Though clearly this is more of a rough guide, than a firm principle.

In the African Wars, as the troops became disorganized, the order was given that no man should venture more than four feet beyond the standards. This illustrates beautifully how the men were expected to orientate themselves by their standards, but it also suggests that, in this case, the standards seem to have been situated very close to the front line.

One of the reasons the men will have paid the standards so much attention when in battle was that they acted as signaling posts. Simple commands were relayed in tandem through the trumpeters, the cornicines and the standard bearers. A blast from the trumpet (cornu) would draw attention to the standard. A number of pre-arranged command signals, such as up and down movements or swaying motions, then visually relayed the order to the ranks.

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The aquila

It appears that standards bearing various animals were used by the legions from earliest times and that they gradually became standardized.
Pliny the Elder suggests the republican army bore five different animal standards, the eagle, the wolf, the minotaur, the horse and the boar.
Marius later made the eagle (aquila) the supreme symbol because of its association with the god Jupiter. The other symbols were subsequently either relegated to a lesser role, or abolished altogether.

In late republican times the eagle standard was most likely silver and a golden thunderbolt was held in the claws of the eagle, but later it was entirely golden. It seems fair to assume though that the above suggests that the eagle was fairly small.
Else, if the eagle atop the standard was rather large, as some seem to suggest, we must assume the animal to have been guilded, as opposed to being of solid gold.

Whilst the eagle was the chief symbol of all legions after Marius, each unit still seemed to entertain several symbols of its own.

These symbols usually referred the date of its foundation, or its founder or a particular commander under whom a great victory had been achieved.
Often therefore the symbols tended to be signs of the zodiac. The connections can be quite complicated.

For example, the goddess Venus was claimed as the mythological ancestor of the Julian family. The bull was held sacred in the worship of Venus. So a bull might denote an association with the Julians.

On the other hand, in the zodiac the bull signifies the period 17th April to 18th May, so a connection might be possible with a date in that period.

I more straightforward example is the use of the Capricorn by the Legio II Augusta, one of the British legions. The legion was founded by emperor Augustus. The Capricorn was an emblem associated with him.
To complicate matters, however, the Legio II Augusta also bore symbols of Pegasus and Mars.

The imago was a peculiar standard of political importance. It linked the legion with the emperor personally.
This standard, bearing the image of the emperor, was carried by the imaginifer. In later times it also may have included portraits other members of the ruling house.

It is worth pointing out that the aquila and the imago were in care of the first cohort.

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The imago

The maniple was a very ancient division of the legion, consisting of two centuries. This unit too had its own standard.

The hand (manus) at the top of this standard no doubt originally had a significance, although it may not have been understood by the later Romans themselves. Military salute ? Divine protection?
The Romans were a people who maintained traditions, even once they had long fallen into obscurity and were no longer understood. So their own ignorance of the meanings behind such symbolism is well possible.
Below the hand was a crossbar from which could be hung wreaths or other decorations and attached to the staff, in vertical array, were various discs, bearing numbers.
The precise nature of these numbers is not understood but they may have been the numbers allocated the unit to identify its cohort, maniple or century.
(e.g. 3rd cohort, 1st maniple, 2nd century)

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The signum

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The vexillum

The one standard that came close to resembling what we recognize as a flag today was the vexillum, a small square piece of cloth attached to a cross-bar carried on a pole.
This type of standard was in general use by the Roman cavalry, most likely as it was lighter and hence less of an encumbrance to the bearer.

The infantry however also made use of the vexillum. It was used for units detached from the main body of an army.
e.g. if a century, or several contubernia were dispatched on a mission, they would carry their own vexillum, as a temporary standard.

The bearer of the vexillum standard, in both infantry and cavalry, was known as the vexillarius

Finally, it is worth noting that all standard bearers wore animal skins over their uniforms and helmets. This seemed to be a very ancient practice, derived from the Celts. The tribe of the Suebi for instance was said to have worn boar masks.